cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A048725 a(n) = Xmult(n,5) or rule90(n,1).

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%I A048725 #32 Jul 06 2022 22:18:55
%S A048725 0,5,10,15,20,17,30,27,40,45,34,39,60,57,54,51,80,85,90,95,68,65,78,
%T A048725 75,120,125,114,119,108,105,102,99,160,165,170,175,180,177,190,187,
%U A048725 136,141,130,135,156,153,150,147,240,245,250,255,228,225,238,235,216,221,210
%N A048725 a(n) = Xmult(n,5) or rule90(n,1).
%C A048725 The orbit of 1 under iteration of this function is the Sierpinski gasket A038183. It is called "rule 90" because the 8 bits of 90 = 01011010 in binary give bit k of the result as function of the value in {0,...,7} made out of bits k,k+1,k+2 of the input (i.e., floor(input / 2^k) mod 8). - _M. F. Hasler_, Oct 09 2017
%H A048725 Alois P. Heinz, <a href="/A048725/b048725.txt">Table of n, a(n) for n = 0..16383</a>
%F A048725 a(n) = n XOR n*2 XOR (n XOR n*2)*2 = A048724(A048724(n)). - _Reinhard Zumkeller_, Nov 12 2004
%F A048725 a(n) = n XOR (4n). - _M. F. Hasler_, Oct 09 2017
%e A048725    n (in binary) | 4n [binary] | n XOR 4n [binary] | [decimal] = a(n)
%e A048725           0      |        0    |           0       |        0
%e A048725           1      |      100    |         101       |        5
%e A048725          10      |     1000    |        1010       |       10
%e A048725          11      |     1100    |        1111       |       15
%e A048725         100      |    10000    |       10100       |       20
%e A048725         101      |    10100    |       10001       |       17
%e A048725    etc.
%p A048725 a:= n-> Bits[Xor](n*4, n):
%p A048725 seq(a(n), n=0..120);  # _Alois P. Heinz_, Aug 24 2019
%t A048725 Table[ BitXor[4n, n], {n, 0, 60}] (* _Robert G. Wilson v_, Jul 06 2006 *)
%o A048725 (PARI) a(n)=bitxor(n,4*n) \\ _Charles R Greathouse IV_, Oct 03 2016
%o A048725 (Python)
%o A048725 def A048725(n): return n^ n<<2 # _Chai Wah Wu_, Jun 29 2022
%Y A048725 Cf. A048720, A048705, A048710, A048724, A048727, A048729.
%Y A048725 Cf. A038183.
%Y A048725 Cf. A353167 (terms sorted).
%K A048725 nonn,easy
%O A048725 0,2
%A A048725 _Antti Karttunen_, Apr 26 1999